Because the third DC has no required items. First, you have to put more chests between DCs, because one inventory cannot treated both as a storage and an inventory to load. Second, you have to build a network, so DCs could pass item requests to other DCs.
Here is manual (Regular Loading topic): https://mods.factorio.com/mod/distribution-centers/discussion/5f79b1f7b36ff79fc9a38cf4
